Factual error: S3E01, "All In", reveals that Winston is colorblind, seeing green as brown. But later in the series, Winston becomes a cop, working for the LAPD. This wouldn't have happened because candidates for the LAPD are put through a color blindness test where they are required to quickly and accurately identify colors. Winston would have failed and would not have been allowed to join the LAPD.
Factual error: There is no HDMI plugged in to the TV, which is accurate for there being no input detected when Coach turns it on to watch the game, but Jess cuts a coaxial cable that is plugged directly into the TV. The input should have been on the Live TV/Antenna/Over-the-Air/Channels input if that's how they watch TV. (00:15:29)